Abstract

Let $$\overline{p}(n)$$ denote the overpartition function. Engel showed that for $$n\ge 2$$ , $$\overline{p}(n)$$ satisfy the Turan inequalities, that is, $$\overline{p}(n)^2-\overline{p}(n-1)\overline{p}(n+1)>0$$ for $$n\ge 2$$ . In this paper, we prove several inequalities for $$\overline{p}(n)$$ . Moreover, motivated by the work of Chen, Jia and Wang, we find that the higher order Turan inequalities of $$\overline{p}(n)$$ can also be determined.

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